Question

Consider the analogy between an oscillating spring-body system and an oscillating L-C-R circuit. Then, the correspondence between the two systems that is NOT correct is:

• A. charge \( q \) corresponds to displacement \( x \) of the body
• B. inductance \( L \) corresponds to mass \( m \) of the body
• C. capacitance \( C \) corresponds to spring constant \( k \)
• D. magnetic energy corresponds to kinetic energy of the body

Hint:

In oscillating systems, the analogies between mechanical and electrical systems help in understanding their dynamics, but some correspondences, like that of the spring constant and capacitance, are often misunderstood.

Answer 1

The Correct Option is C

In an oscillating spring-body system and an oscillating L-C-R circuit, there are several analogies between the two systems.
These analogies are based on the nature of the oscillations in both systems: - The charge \( q \) in the L-C-R circuit corresponds to the displacement \( x \) of the body in the spring system.
This is because both quantities describe the position of the system at any given time. - The inductance \( L \) in the L-C-R circuit corresponds to the mass \( m \) of the body in the spring system, as both terms are related to inertia in the respective systems. - The capacitance \( C \) in the L-C-R circuit corresponds to the spring constant \( k \) in the spring-body system.
However, this analogy is incorrect.
In fact, the spring constant \( k \) is related to the restoring force in the spring-body system, while the capacitance \( C \) in the L-C-R circuit relates to the storage of energy in the electric field of the capacitor.
The correct analogy is that the spring constant corresponds to the inverse of the capacitance. Therefore, the correct answer is (c).